Proceedings Third UJNR Workshop on Soil-Structure Interaction, March 29-30, 2004, Menlo Park, California, USA.

Transcription

1 Proceedings Third UJNR Workshop on Soil-Structure Interaction, March 29-30, 2004, Menlo Park, California, USA. Variability of Soil-Structure System Frequencies during Strong Earthquake Shaking for a Group of Buildings in Los Angeles Estimated from Strong Motion Records Maria I. Todorovska, a) Tzong-Ying Hao, a) and Mihailo D. Trifunac a) Most seismic building codes estimate the design forces in structures based on the seismic coefficient C(T), where T is the fundamental vibration period of the building. For structures on flexible soil, T is the first period of the soil-structure system, which depends on the structure itself, but also on the foundation system, surrounding soil, and contact conditions between the foundation and the soil. This paper presents results of instantaneous system frequency as function of the level of response for seven buildings in the Los Angeles area that have recorded several earthquakes 1994 earthquake (M S = 6.7) and aftershocks, and 1971 San Fernando earthquake (M S = 6.6). In general, the observed trend is decrease of system frequency during 1994 and 1971 San Fernando earthquakes, which caused the largest levels of response, and recovery during the aftershocks. For one of the buildings, a significant change (30% reduction) that occurred during the San Fernando earthquake appears to have been permanent. For most buildings, the frequency changed up to 20%, and for two buildings, the change was about 30%. Understanding and estimation of the range of these variations during strong earthquake shaking is needed for further refinement of the existing and development of new design code procedures. INTRODUCTION The Earthquake Resistant Design Codes have evolved based on principles and procedures derived from the Response Spectrum Method (Biot, 1942). In most codes, the design shear forces are quantified using the seismic coefficient C(T), where T is the fundamental vibration period of the building, and various scaling factors that depend on the seismic zone, type of structure, soil site conditions, importance of the structure etc. As T a) Civil Engineering Department, University of Southern California, Los Angeles, CA

2 cannot be measured before the structure is completed, most codes provide simplified empirical formulae to estimate it, based on past experience and recorded response of existing buildings, which is extremely limited (both in quantity and in quality). The problem of estimation of T has been considered by many investigators, based on theory (Biot, 1942), small amplitude ambient and forced vibration tests of full-scale structures (Carder, 1936), and recorded earthquake response in structures (Li and Mau, 1979). Unfortunately, the number of well-documented instrumented buildings that have recorded at least one earthquake is typically less than 100. When the recorded data is grouped by structural systems (moment resistant frame, shear wall etc.) and building materials (reinforced concrete, steal, etc.), the number of records per group becomes too small to control the accuracy of regression analyses, or to separate good from bad empirical models (Goel and Chopra, 1997; Stewart et al., 1999). This problem is further complicated by the nonlinearity of the foundation soil even for very small strains (Hudson, 1970; Luco et al., 1987). During strong earthquake shaking, the apparent period of the soil-foundation-structure system, T, can lengthen significantly (Udwadia and Trifunac, 1974), and it may or may not return to its pre earthquake value. This period lengthening can reach and exceed a factor of two, which adds to the scatter in the empirical regression analyses, and to the ambiguity in choosing a representative T for evaluation of C(T) (Trifunac, 1999; 2000). For further improvements and developments of the building codes, it is essential to understand the amplitude dependent period lengthening (as function of the level of response of the structure and strain in the soil), and estimate its range, which can be best accomplished by analysis of building periods from multiple earthquake recordings in buildings of both small and large levels of shaking. The first step towards this goal is to augment the database of multiple earthquake records in buildings, which is very limited, because most buildings records have been recorded on film, and, mostly those with larger amplitudes have been digitized and released. Data of small amplitude response will be generated fast from instrumented buildings with a digital recording system, but it may take many years for these systems to record larger amplitude response. Hence, the use of small amplitude data from newly instrumented buildings is quite limited. Data of smaller amplitude response has been recorded digitally in some buildings complementing larger amplitude response data recorded previously by an analog recording system. In these cases, smaller amplitude analog recordings of past earthquakes are also very valuable for understanding of the variations of building periods with time, which may be temporary or permanent. In the Los Angeles 2

3 metropolitan area, there have been many small earthquakes and aftershocks of larger earthquakes that have been recorded in buildings and archived but not digitized and released. An effort was initiated at the University of Southern California to augment the database of building periods estimated from multiple earthquake recordings, with the immediate objective to trace their variations with time and as a function of the level of response and understand their nature, and with the ultimate objective to improve the code formulae for estimation of building periods. This paper presents a summary of results of a one year effort, which consisted of digitization and processing of building records from the archives of the U.S. Geological Survey (USGS), gathering of already processed data for the same buildings, and analysis of the building period. Results are shown of the variation of the building apparent frequency (i.e. building-foundation-soil system frequency) as a function of the level of response for seven buildings in the Los Angeles area, which recorded the earthquake and some of its aftershocks. The records in these seven buildings that have been digitized and processed for this project are those of aftershocks of the 1994 earthquake as well as those of the main event that have not been digitized previously or have been redigitized for this project. These buildings have been instrumented either by USGS or by the building owner. Detailed results and a catalog of the processed data can be found in Todorovska et al. (2004) and the processed data is available from the USC Strong Motion Research Group web site at STRONG MOTION DATA Figure 1 shows a map of the Los Angeles metropolitan area and locations of buildings that were instrumented at the time of the 1994 earthquake, either by the USGS and partner organizations, or by the building owners (as required by the Los Angeles and state building codes), for which the data is archived by USGS. The latter are often referred to as code buildings. All of these buildings will be referred to as USGS instrumented buildings and identified by their station number. The sensors in these buildings have been either three-component SMA-1 or multichannel CR-1 accelerographs, both recording on film. Many of the code buildings (about 30 buildings total) have only one instrument, at the roof, due to a change in the original ordinance for Los Angeles, such that only one instrument at the roof was required, which lead to removal or neglect of the instruments at the ground floor and intermediate levels. 3

4 This unfortunate fact limits considerably the use of these records, especially for analyses of soil-structure interaction. The roof records can be used to estimate the apparent building period, by approximating the relative roof motion (with respect to the base) by the absolute roof motion. After the earthquake, the analog strong motion instrumentation is being gradually replaced by digital, and additional buildings are being instrumented. For some of these buildings, data of smaller local earthquakes and distant larger earthquakes has been recorded and released. The recorded level of response for these events, however, is much smaller than that for the earthquake. Figure 1 also shows the epicenters of earthquakes that have been recorded in these buildings. The main event was followed by a large number of aftershocks (9 of these had M > 5, and 55 had M > 4). Many of these larger magnitude aftershocks, as well as smaller magnitude but closer aftershocks, were recorded in the instrumented buildings. The aftershock of March 20, 1994 (M = 5.2; aftershock 392 ) was the one recorded by the largest number of (ground motion) stations (Todorovska et al., 1999). The sequence was recorded on multiple films, archived separately. The largest number of recorded aftershocks known to the authors of this paper is 86 at station USGS #5455, and about 60 at several other stations. Unfortunately, it turned out that the number of aftershock records useable for estimation of the building apparent frequency was small up to 11. The usability of an aftershock record for estimation of the first system frequency depends not only on its amplitudes, but also on the shape of its Fourier spectrum, and on the building itself, i.e. on how high is its first system frequency. In principle, a building record is useable if the first system frequency is within the useable frequency band of the signal, which is the band where the Fourier spectrum of the signal is above that of the recording and digitization noise, and below the Nyquist frequency. While the high-frequency limit of this band is controlled by the Nyquist frequency, the low-frequency limit is controlled by the noise spectrum, which increases with decreasing frequency and is due to a wavy baseline. These limits are determined automatically by standard software for accelerogram data processing (Lee and Trifunac, 1990), which then band-pass filters the digitized accelerogram. In this study, if the first system frequency was too close to, or was suspected to be below the low-frequency cut-off of the data processing software, the record was discarded. A record was also discarded if the system frequency could not be estimated reliably for some other 4

5 reason. This selection process eliminated many aftershock records. In summary, small aftershock records are more likely to be useable for the shorter buildings, than for the taller ones. Also, for the taller buildings, the records from large but distant earthquakes (like 1992 Landers) are more likely to be useable than those from small nearby events with similar peak acceleration, because the former have more energy in the shorter frequency part of the spectrum and will excite more the first mode, leading to larger signal to noise ratio at low frequencies. Therefore, it is important to digitize and add to the analysis good records of the 1992 Landers and 1999 Hector Mine earthquakes San Fernando Valley San Fernando 1972 San Gabriel Mountains km Sierra Madre, Pasadena, Los Angeles and Aftershocks Whittier Narrows and Aftershocks Santa Monica Malibu, 1989 Pacific Ocean West Hollywood Montebello, S. California San Pedro USGS instrumeneted building sites analysis completed and reported analysis to be completed after additional data is processed other USGS instrumeneted buildings Long Beach Figure 1. Locations of instrumented buildings in the Los Angeles metropolitan area at the time of the 1994 earthquake, for which the data is archived by USGS The building sites are identified by their USGS station number. 5

6 This paper shows results for 7 buildings for which there were three or more adequate records (of the sequence or of the 1971 San Fernando earthquake) to estimate the apparent building frequency, and for which there are no other good records to add to the analysis, so that the analysis is complete. These stations are marked by solid dark dots in Fig. 1. For the 15 stations marked by solid light dots, there are some adequate records of the sequence, as well as other good records that have not yet been digitized (e.g. of the Landers and/or of the Whittier-Narrows earthquake). For the other buildings, marked in Fig. 1 by solid rectangles, at this time, only one or maybe two adequate records for such analysis are known to exist, and are not included in this analysis. Table 1 shows a list of earthquakes recorded in USGS instrumented buildings. For the sequence, only the aftershocks are shown for which there is an adequate record that has been used in the analysis presented in this paper. For most of the buildings, the contributing aftershocks have not been identified, but are assigned negative aftershock number, the absolute value of which increases chronologically, and is related to the order of the record on the film (e.g., aftershock 3 means that this was the third aftershock record on the film following the main event, and aftershock 105 means that this was the fifth record on the second role of film, which did not contain the main event). This table also lists the 2001 West Hollywood earthquake (M = 4.2), which occurred close to many of the instrumented buildings (see Fig. 1), and which should have been recorded by these buildings. Table 2 shows a list of buildings included in the analysis in this paper. The processed data (uncorrected acceleration, corrected acceleration, velocity and displacement, and Fourier and response spectra) is available free of charge from the USC Strong Motion Research Group web site at METHODOLOGY The instantaneous frequency was estimated by two s: (a) zero-crossing analysis, and (b) from the ridge of the Gabor transform, both applied to the relative roof displacement when there was a record at the base, or to the absolute displacement when only the roof response was recorded, and considered as an approximation of the relative displacement in the neighborhood of the first system frequency. Both s were applied to the filtered displacement, such that it contained only motion in the neighborhood of the first system frequency, and resembled a chirp signal. The zero-crossing analysis consists of measuring 6

7 Table 1. Earthquakes recorded by USGS instrumented buildings (1971 to 2001). Event Date Time M L Latitude Longitude Depth (km) San Fernando 02/09/ : N W -- Whittier-Narrows 10/01/ : N W 14.5 Whittier-Narrows, 12 th Aft. 10/04/ : N W 13.0 Whittier-Narrows, 13 th Aft. 02/03/ : N W 16.7 Pasadena 12/03/ : N W 13.3 Malibu 01/19/ : N W 11.8 Montebello 06/12/ : N W 15.6 Upland 02/28/ : N W 5.3 Sierra Madre 06/28/ : N W 12.0 Landers 06/28/ : N W 5.0 Big Bear 06/28/ : N W /17/ : N W 18.4, Aft. #1 01/17/ : N W 0.0, Aft. #7 01/17/ : N W 14.8, Aft. #9 01/17/ : N W 0.0, Aft. #100 01/17/ : N W 19.2, Aft. #129 01/17/ : N W 9.5, Aft. #142 01/17/ : N W 9.8, Aft. #151 01/18/ : N W 11.3, Aft. #253 01/19/ : N W 14.4, Aft. #254 01/19/ : N W 11.4, Aft. #336 01/29/ : N W 1.1, Aft. #392 03/20/ : N W 13.1 Hector Mine 10/16/ : N W 3.0 West Hollywood 09/09/ : N W 3.7 Table 2. USGS instrumented buildings included in the analysis. USGS: 0466, SMA Los Angeles, Ventura Blvd., Roof (13th floor) N, W USGS: 5108 SMA 1276 and 1277 Canoga Park, Santa Susana, ETEC Bldg 462 (6th and 1st floors) N, W USGS: 5450, SMA Burbank, 3601 West Olive Ave., Roof (9th floor) N, W USGS: 5451, SMA Los Angeles, 6301 Owensmouth Ave., Roof (12th level) N, W USGS: 5453, SMA Los Angeles, 5805 Sepulveda Blvd., Roof (9th floor) N, W USGS: 5455, SMA Los Angeles, Ventura Blvd., Roof (13th floor) N, W USGS: 5457, SMA 5491 LOS ANGELES, 8436 WEST 3rd ST., Roof (10th floor) N, W 7

8 the time between consecutive zero crossings of the displacement, and assuming this time interval to be a half of the system period (see Trifunac et al., 2001a, 2001b, 2001c). The Gabor transform is a time-frequency distribution, which is up to a phase shift identical to a moving window analysis with a Gaussian time window. The instantaneous frequency was determined from the ridge of the transform, and the corresponding amplitude was estimated from the skeleton of the transform, which is the value of the transform along the ridge (see Todorovska, 2001). The wavelet transform with the complex Morlet wavelet was initially considered, which is essentially a Gabor transform with a window that varies depending on the frequency, so that it always contains same number of wavelengths. The results by both s were found to be very similar, and no advantage was seen in using a variable window because the changes of the building frequency are relatively small, much smaller than an order of magnitude. Using constant window was convenient in the estimation of the resolution of the. The Gabor transform was used with spread σ = 1.5. Figure 2 shows the Gabor wavelet and its Fourier transform. Gabor wavelet, ω=2π, σ= g (b,ω) (t) 3 g (b,ω) (ξ) σ t t s ξ/(2π) Hz Figure 2 A Gabor wavelet for time shift b = 0 and ω = 2π, in the time domain (left) and in the frequency domain (right). The ology for estimation of the instantaneous frequency of building-soil systems is illustrated in Fig. 3, parts a and b, respectively for two records component N11E of the record of the 1971 San Fernando earthquake at station USGS 466 (Los Angeles, Ventura Blvd.), and component N00E of the record of the 1994 earthquake at station USGS 5453 (Los Angeles, 5805 Sepulveda Blvd.). For each record, the plot on the left hand side shows the Fourier spectrum of the relative roof displacement (solid line), or its approximation by the absolute displacement when only a roof record was available, the 8

9 Fourier spectrum of acceleration at the ground floor (dashed line) if available, and a smooth approximation of the relative (or absolute) roof displacement spectrum by the marginal Gabor transform distribution (the smooth line). There are three plots in the right hand side, as follows. The plot on the top shows the time history of the roof relative (or absolute) displacement (solid line), and of the ground floor displacement (dashed line) if available, for the broad-band data, which is the output of the standard data processing. The plot in the middle shows the same time histories but for the narrow-band data, which is the broadband data filtered so that it contains only the frequencies in the neighborhood of the first building-soil system frequency. The cut-off and role-off frequencies, in Hz, of the Ormsby filters used are shown in the upper right corner of these plots. The plot in the bottom shows the instantaneous frequency versus time estimated by the zero-crossing analysis (open circles), and Gabor analysis (with σ = 1.5 for all the records). The shaded rectangle in this plot has width 2σ t and height 2σ ω and is a measure of the resolution of the Gabor analysis. The Gabor transform at a point ( t, f ) in the time frequency plane is the weighed average of the components of the function (effectively) within such a rectangle centered at that point. The cannot resolve frequencies that are closer than σ ω, and estimates in time that are closer than σ t. The resolution in frequency can be increased only if the resolution in time is decreased (by increasing the time window of the Gabor wavelet, and consequently σ ), and vice versa. The results in Fig. 3 show that the estimates by the zero-crossing and Gabor analyses are consistent. The estimates by the latter are smoother, as the Gabor transform is a smoothing operator. The zero-crossing analysis is not accurate when the oscillations of the signal depart too much from a pure harmonic, and these estimates are not shown. Both s are most accurate when the amplitude of the signal is large and does not vary significantly during one cycle of oscillation, least accurate when the amplitude is small and varies significantly during one cycle, and are arbitrary when the amplitude is practically zero. A significant change (decrease) in the system frequency of about 30% during a single earthquake is seen for both buildings. t 9

10 a) b) Figure 3. Estimation of the instantaneous frequency for a) component N00E of the record of the 1994 earthquake at station USGS 5453 (Los Angeles, 5805 Sepulveda Blvd.), and b) component N11E of the record of the 1971 San Fernando earthquake at station USGS 466 (Los Angeles, Ventura Blvd.). 10

11 RESULTS Figures 4 through 10 show, in a compact form, results for the variation of the buildingsoil system frequency in time as function of the amplitude of response for the seven buildings. Detailed results, like those in Fig. 3, for every earthquake and component of motion, can be found in Todorovska et al. (2004). Each of these figures shows four plots, as follows. Those on the top correspond to one of the two horizontal component of motion, and those on the bottom to the other horizontal component of motion, while those on the left correspond to estimates by zero-crossing analysis, and those on the right by Gabor analysis. In each plot, the horizontal axis corresponds to the instantaneous frequency, the vertical axis corresponds to the amplitude of response (of the filtered signal) expressed as a rocking angle in radians, and each point corresponds to a particular instant in time. The rocking angle was computed by dividing by the distance between the top and bottom instruments, estimated using average floor height of 12.5 feet (1 foot=30.48 cm) the amplitude of the relative (roof minus base) response, if motion at the base was recorded, or otherwise the absolute horizontal response of the roof or top floor. It is noted here that this rocking angle includes the rigid body rocking, which could not be separated because of insufficient number of instruments at the base, in addition to motion resulting from deflection of the structure. In Figs 4 through 10, the points corresponding to consecutive instants of time are connected by a line, each line corresponding to a particular earthquake. In the plots showing results from the zero-crossing analysis, the first and last point shown for a particular earthquake are marked respectively by an open and a closed circle. The backbone curve, drawn by hand, indicates roughly the trend of the variation of the system frequency as function of the amplitude of response. It can be seen that for the largest motions (during the 1971 San Fernando and 1994 earthquakes), the system frequency generally decreased during the shaking. For all but one building, this change seems to have been temporary, as the system frequency increased during the shaking by the aftershocks. For one building, permanent change appears to have occurred during the 1971 San Fernando earthquake (USGS 466). Detailed interpretation of the causes of these changes is beyond the scope of this project. The maximum and minimum frequencies determined from the backbone curves in Figs 4 through 10, and the corresponding maximum and minimum levels of response, are summarized in Table 3 and the percentage change for all the seven buildings 11

12 Rocking angle (rad) Rocking angle (rad) USGS 0466: Sherman Oaks, Ventura Blvd N-S (Longitudinal) Zero-crossing N-S (Longitudinal) Gabor transform San Fernando (1971) San Fernando (1971) aft. -1 aft E-W (Transverse) Zero-crossing E-W (Transverse) Gabor transform San Fernando (1971) San Fernando (1971) aft. -1 aft Instantaneous frequency, f p Instantaneous frequency, f p Figure 4. Instantaneous frequency versus amplitude of motion for station USGS

13 Rocking angle (rad) Rocking angle (rad) USGS 5108: Canoga Park, Santa Susana - ETEC Bldg #462 E-W Comp. Zero-crossing E-W Comp. Gabor transform Aft. 129 Aft. 253 Aft. 129 Aft. 253 Aft. 336 Aft. 336 Aft. 142 Aft Aft. 392 Aft. 100 Aft. 392 Aft. 9 Aft. 7 Aft. 254 Aft. 100 Aft. 9 Aft. 7 Aft N-S Comp. Zero-crossing N-S Comp. Gabor transform Aft. 336 Aft. 151 Aft. 129 Aft. 142 Aft. 129 Aft. 151 Aft Aft. 253 Aft. 392 Aft. 253 Aft. 336 Aft. 392 Aft. 9 Aft Instantaneous frequency, f p Instantaneous frequency, f p Figure 5. Instantaneous frequency versus amplitude of motion for station USGS

14 Rocking angle (rad) Rocking angle (rad) 10-2 USGS 5450: Burbank, 3601 West Olive Ave. N00E Zero-crossing N00E Gabor transform Aft. -1 Aft. -13 Aft. -1 Aft. -13 Aft. -5 Aft. -14 Aft. -14 Aft W00N Zero-crossing W00N Gabor transform Aft. -1 Aft. -13 Aft. -1 Aft. -5 Aft. -13 Aft. -5 Aft. -14 Aft Instantaneous frequency, f p Instantaneous frequency, f p Figure 6. Instantaneous frequency versus amplitude of motion for station USGS

15 Rocking angle (rad) Rocking angle (rad) USGS 5451: Los Angeles, 6301 Owensmouth Blvd N00E (Transverse) Zero-crossing N00E (Transverse) Gabor transform Aft. -26 Aft. -26 Aft Aft W00N (Longitudinal) Zero-crossing W00N (Longitudinal) Gabor transform 10-2 Aft. -26 Aft. -26 Aft Aft Apparent frequency, f p Apparent frequency, f p Figure 7. Instantaneous frequency versus amplitude of motion for station USGS

16 Rocking angle (rad) Rocking angle (rad) USGS 5453: Van Nuys, 5805 Sepulveda Blvd N00E Zero-crossing N00E Gabor transform Aft. -1 Aft. -1 Aft. -7 Aft. -29 Aft. -29 Aft W00N Zero-crossing W00N Gabor transform Aft. -26 Aft. -29 Aft. -26 Aft. -7 Aft Aft Aft. -24 Aft. -29 Aft Aft. 24 Aft Aft Aft. -7 Aft Instantaneous frequency, f p Instantaneous frequency, f p Figure 8. Instantaneous frequency versus amplitude of motion for station USGS

17 Rocking angle (rad) Rocking angle (rad) 10-2 USGS 5455: Los Angeles, E30S Zero-crossing Ventura Blvd. E30S Gabor transform Aft. -1 Aft. -1 Aft. -25 Aft. -46 Aft. -25 Aft. -46 Aft. -7 Aft N30E Zero-crossing N30E Gabor transform Aft. -1 Aft. -25 Aft. -25 Aft. -1 Aft. -46 Aft. -22 Aft. -46 Aft Instantaneous frequency, f p Instantaneous frequency, f p Figure 9. Instantaneous frequency versus amplitude of motion for station USGS

18 Rocking angle (rad) Rocking angle (rad) USGS 5457: Los Angeles, 4836 West 3rd St N00E Zero-crossing N00E Gabor transform Aft. 9 Aft. 19 Aft. 19 Aft. 1 Aft. 9 Aft. 1 Aft. 10 Aft. 13 Aft. 10 Aft. 13 Aft. 4 Aft. 8 Aft. 4 Aft S90W Zero-crossing S90W Gabor transform Aft. 8 Aft. 8 Aft. 19 Aft. 9 Aft. 4 Aft. 9 Aft Aft. 4 Aft. 17 Aft. 10 Aft. 19 Aft Apparent frequency, f p Apparent frequency, f p Figure 10. Instantaneous frequency versus amplitude of motion for station USGS

19 USGS 5450 USGS 5108 USGS 5451 USGS 5455 USGS 5457 USGS 0466 USGS 5453 Table 3. Maximum and minimum system frequencies and maximum and minimum rocking angles for seven instrumented buildings. Station no. Comp., f / (%), ( rad) Comp., f / (%), ( rad) 5108 E00S 2.130, , N00E 1.899, , N00E 0.377, , W00N 0.295, , N00E 0.691, , W00N 0.666, , N00E 0.329, , W00N 0.434, , N00E 0.613, , W00N 0.744, , E30S 0.434, , N30E 0.425, , N00E 0.675, , S00W 0.866, , f (%) Figure 11. A summary of the changes of the building-soil system frequencies of the seven buildings analyzed in this paper, determined from the observed trends during multiple earthquake excitations (see Figures 4.1 through 4.24). For each building, two values are shown, corresponding to the two horizontal components of motion. The change is expressed as a percentage of the maximum frequency. is shown in Fig. 11. It is seen that, for these levels of response, the change for most of the buildings is not more than 20%, but it reaches 30% for two of the buildings. 19

20 SUMMARY AND CONCLUSIONS This paper presents results for apparent building frequency for seven buildings in the Los Angeles area that have recorded the 1994 earthquake and some of its aftershocks. Although the number of recorded aftershocks in these buildings was large (up to about 80), only a small number of records were found to be useable for this analysis, because of the small signal to noise ratio at long periods which lead to high lower cut-off frequency, higher or too close to the system frequency. The system frequency was estimated by two s zero crossing and Gabor analyses. The results by both s are consistent. The general observed trend of the variation of the system frequency is decrease during the 1994 main event, and the 1971 San Fernando earthquake, which caused the largest amplitude response. For all but one building, the frequency was again larger during the aftershocks, indicating system recovery. For most buildings, the frequency changed up to 20%, and for two buildings, the change was about 30%. A permanent reduction of the frequency is consistent with permanent loss of stiffness, while a recovery to the initial higher value is consistent with the interpretation that the change was mainly due to changes in the soil (rather than in the structure itself), or changes in the bond between the soil and the foundation. Other possible causes of the temporary changes are: contribution of the nonstructural elements to the total stiffness in resisting the seismic forces, and opening of existing cracks in the concrete structures during larger amplitude response. The degree to which each of these causes contributed to the temporary changes cannot be determined from the current instrumentation and is beyond the scope of this analysis. What matters for the design codes, however, is the overall effect, which can be estimated even from the minimum (roof only) building instrumentation. ACKNOWLEDGEMENTS This work was supported by U.S. Geological Survey External Research Program (Grant No. 03HQGR0013). All views presented are solely those of the authors and do not necessarily represent the official views of the U.S. Government. The authors are also grateful to Chris Stephens of the U.S. Geological Survey for kindly supplying film records for this project from the National Strong Motion Program archives. 20

21 REFERENCES Biot, M.A., Analytical and experimented s in engineering seismology, Trans., ASCE, 68, Carder, D.S., Vibration observations, Chapter 5, in Earthquake Investigations in California , U.S. Dept. of Commerce, Coast and Geological Survey, Special Publication No. 201, Washington D.C. Goel, R.K. and A.K. Chopra, Period formulas for concrete shear wall buildings, J. of Structural Eng., ASCE, 124(4), Hudson, D.E., Dynamic tests of full scale structures, Chapter 7, , in Earthquake Engineering, Edited by R.L. Wiegel, Prentice Hall, N.J. Lee, V.W. and M.D. Trifunac, Automatic digitization and processing of accelerograms using PC, Report No , Dept. of Civil Engrg, U. of So. California, Los Angeles, CA. Li, Y. and S.T. Mau, Learning from recorded earthquake motions in buildings, J. of Structural Engrg, ASCE, 123(1), Luco, J.E., M.D. Trifunac and H.L. Wong, On the apparent change in dynamic behavior of a nine story reinforced concrete building, Bull. Seism. Soc. Amer., 77(6), Stewart, J.P. R.B. Seed and G. L. Fenves, Seismic soil-structure interaction in buildings II: Empirical findings, J. of Geotechnical and Geoenvironmental Engrg, ASCE, 125(1), Todorovska, M.I., Estimation of instantaneous frequency of signals using the continuous wavelet transform, Report CE 01-07, Dept. of Civil Engrg., Univ. of Southern California, Los Angeles, California. Todorovska, M.I., T-Y. Hao, and M. D. Trifunac, Building periods for use in earthquake resistant design codes earthquake response data compilation and analysis of time and amplitude variations, Report CE 04-02, Dept. of Civil Engrg., Univ. of Southern California, Los Angeles, California. Todorovska, M.I., M.D. Trifunac, V.W. Lee, C.D. Stephens, K.A. Fogleman, C. Davis and R. Tognazzini, The ML = 6.4, California, Earthquake and Five M > 5 Aftershocks Between 17 January and 20 March Summary of Processed Strong 21

22 Motion Data, Report CE 99-01, Dept. of Civil Engrg., Univ. of Southern California, Los Angeles, California. Trifunac, M.D., Comments on Period formulas for concrete shear wall buildings, J. Struct. Eng., ASCE, 125(7), Trifunac, M.D., Comments on Seismic soil-structure interaction in buildings I: analytical models, and II: empirical findings, J. of Geotechnical and Geoenvironmental Engrg, ASCE, 126(7), Trifunac, M.D., T.Y. Hao & M.I. Todorovska, 2001a. On energy flow in earthquake response, Report CE 01-03, Dept. of Civil Engrg., Univ. of Southern California, Los Angeles, California. Trifunac, M.D., T.Y. Hao & M.I. Todorovska, 2001b. Energy of earthquake response as a design tool, Proc. 13th Mexican National Conf. on Earthquake Engineering, Guadalajara, Mexico. Trifunac, M.D., M.I. Todorovska and T.Y. Hao, 2001c. Full-scale experimental studies of soil-structure interaction - a review, Proc. 2nd UJNR Workshop on Soil-Structure Interaction, March 6-8, 2001, Tsukuba City, Japan, pp. 52. Udwadia, F.E. and M.D. Trifunac, Time and amplitude dependent response of structures, Earthquake Engrg and Structural Dynamics, 2,